This exercise is on probabilities and coincidence of shared birthdays. Complete

ID: 3049960 • Letter: T

Question

This exercise is on probabilities and coincidence of shared birthdays. Complete parts(a) through(d) below

a. If six people are selected at random, find the probability that they all have different birthdays.

b. If six people are selected at random, find the probability that at least two of them have the same birthday.

c. If 19 people are selected at random, find the probability that at least 2 of them have the same birthday.

d. Show that if 23 people are selected at random, the probability that at least 2 of them have the same birthday is greater than 1/2.

a) probability that they all have different birthdays =(365/365)*(364/365)*(363/365)*(362/365)*(361/365)*(360/365)

=0.959538

b) probability that at least two of them have the same birthday =1-P(none have same birthday )=1-0.959538

=0.040462

probability that at least 2 of them have the same birthday=1-P(none of 19 have same brthday)

-(365/365)*(364/365)*(363/365)*..... *(347/365)=1-620881 =0.379119

probability that at least 2 of them have the same birthday=1-P(none of 23 have same brthday)

-(365/365)*(364/365)*(363/365)*..... *(343/365)=1-0.492703 =0.507297 whcih is greater than 1/2.

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